Abstract

We consider a restricted three-body problem consisting of two positive equal masses m 1 = m 2 moving, under the mutual gravitational attraction, in a collision orbit and a third infinitesimal mass m 3 moving in the plane P perpendicular to the line joining m 1 and m 2. The plane P is assumed to pass through the center of mass of m 1 and m 2. Since the motion of m 1 and m 2 is not affected by m 3, from the symmetry of the configuration it is clear that m 3 remains in the plane P and the three masses are at the vertices of an isosceles triangle for all time. The restricted planar isosceles three-body problem describes the motion of m 3 when its angular momentum is different from zero and the motion of m 1 and m 2 is not periodic. Our main result is the characterization of the global flow of this problem. © 2009 Springer Science+Business Media B.V.